Sinusoidal steady-state field exists widely in power transmission and transformation system and other practical engineering. In the case of two dimensions (2-D), the calculation formula for the maximum of the field vector has been proposed and the study on the endpoint trajectory of field vector has been completed. However, further research on three dimensional (3-D) Sinusoidal steady-state field vector is required to compute the maximum and understand the endpoint trajectory. In this paper, analytical formulas for the maximum and minimum of 3-D sinusoidal steady-state field vector have been deduced based on phasor. It is demonstrated that the endpoint trajectory is an elliptical orbit in 3-D space by coordinate transformation. The availability of the formulas is verified by comparing the numerical method and the formula results. The application of the formulas presented here results in important computation convenience and time savings.